For some years, until it grew too yellow and curled, I had a New Yorker cartoon taped to my fridge door. In the cartoon, a middle-aged man and a middle-aged woman are conversing at a cocktail party. The woman is asking: "One question. If this is the information age, how come nobody knows anything?"

In Britain, people of that generation make remarks of that kind quite a lot in August. While the school system belches forth the latest A-Level and GCSE results, the usual suspects queue up to say the usual things from their respective viewpoints. The pupils say they are thrilled, the teachers that they are vindicated, education ministers that the system works, and the Daily Telegraph that civilisation is at an end. Amid this annual ritual you can be sure that someone will also say that, while kids today are schooled to pass exams, they lack the broad education and general knowledge that we, their parents, once enjoyed.

My instinct is that a bit of caution is in order before we regurgitate too readily the idea that we of the older generation know so much and our children know so little. I say this partly because I'm often struck by the amount my children know that I don't - and partly because, with the obvious exception of Nicole Kidman, we're none of us perfect anyway.

A group of us, all intelligent, well-educated and middle-aged, were sitting around the table just the other day when I mentioned a fact I am always surprised is so little-known. And guess what? None of the rest of the group knew anything about it either. This week I asked a few colleagues at random what this thing meant to them. Once again, I drew a blank.

So here is my question. What does the word Towton mean to you? If you have the answer, as lots of you will, I'm glad, because you should. Yet if you don't, you are in very good company. It nevertheless says something about us as a nation that you are far more likely not to know anything about Towton than to know instantly what it is.

And here is the answer. Towton is a village about 10 miles south-west of York. It owes what fame it has to the fact that it was once the scene of a battle. But this was not just any battle. At the battle of Towton, more English people were killed than on any other day ever. And by ever I mean - ever.

It is often said that the bloodiest day in our history was July 1 1916, the first day of the Battle of the Somme, when 19,200 soldiers went over the top and were mown down by German guns. As a result, the Somme has become synonymous with the frightful, mindless slaughter of a whole generation of young British men. It traumatised the survivors so much that they barely spoke of it. But it hangs over our country still, nearly a century later. Merely to think of it can make one weep.

Yet Towton was bloodier than the Somme. When night fell on March 29 1461 - it was Palm Sunday, and much of the battle took place in a snowstorm - the Yorkist and Lancastrian dead numbered more than 20,000. It should be said that the figures are much disputed and rise to as many as 28,000 in some accounts, and there were countless wounded besides.

Now remember two other things while you absorb that. First, that while the population of Britain in 1916 was more than 40 million, that of England in 1461 was considerably less than 4 million, so the proportionate impact on the country must have been seismic. One in every hundred Englishmen died at Towton. Its impact must have been a bit like an English Hiroshima.

And, second, that, this being 1461, not a shot was fired. This was not industrial killing from a distance. Every Englishman who died at Towton was pierced by arrows, stabbed, bludgeoned or crushed by another Englishman. As a scene of hand-to-hand human brutality on a mass scale, Towton has absolutely no equal in our history. It was our very own day of wrath.

Towton is not a secret. It is in the books and on the maps. If you visit, there is a memorial. The same river which was so packed with corpses that men fled across them from one bank to the other still runs through it. If you study the Wars of the Roses, you learn it was a decisive Yorkist victory. If you go online you can discover some of the detective work done by the University of Bradford on mutilated skeletons exhumed from some of Towton's mass graves. And if you go to a performance of Henry VI Part 3, you will see that the national poet himself set potent scenes at Towton, where, in the thick of battle, a father finds he has killed his son and a son that he has killed his father, and where the watching and hapless Lancastrian king wishes himself among the dead - "For what is in this world but grief and woe?"

Yet, though not a secret, Towton is largely now forgotten. It carries none of the civic weight that Gettysburg does in America. Of course, Towton was all much longer ago, though more distant Hastings is still recalled well enough. Perhaps the dynastic cause in which Towton was fought is simply too obscure, though plenty of people today can recall roughly what the much later internecine battle at nearby Marston Moor was about.

Towton undoubtedly meant something to Shakespeare and his audiences. He uses it to warn against the great fear of all Tudors, the catastrophe of civil strife. We have no fear of civil war today. Such things belong to the past, where they did things differently. And yet ... Might something other than the fact that it all happened a long time ago partly explain our sustained expunging of Towton from the national memory?

Perhaps Towton is simply too brutal, too senseless and thus too traumatic to acknowledge today. I wonder whether Towton denial is even something we inherit in our DNA, an experience we do not want to confront because its intensity and slaughter do not fit with our island story, our national self-esteem and our enduring need for meaning and optimism. Yet when I think about the mindless killings of our own times, whether at home in the streets of Liverpool or abroad in the bombing of distant cities and villages, it seems clear that something of the savage spirit of Towton still lives on within us, even today - and that we should know about it.